The present invention relates to wireless communications and, more particularly, to an efficient square-root free 2 symbol max-log receiver.
In several communication scenarios the following receiver (demodulator) design problem is ubiquitous. Consider a received signal vector z that has 2 complex-valued elements and can be expressed as:z=Hs+n  (Equation)
where, s is the transmit symbol vector having 2 complex-valued elements, each drawn from a normalized constellation. The matrix H models the channel and the vector n models the additive independent noise, assumed to have complex Gaussian elements of unit variance. Then given z and H and the constellation(s) from which the elements of s are drawn, the receiver (demodulator) design problem is to determine the optimal hard decision about s and/or the optimal soft decisions (log-likelihood ratios) about the coded bits mapped to s.
One approach to solving the above problem, the brute-force way, to determine either the hard or soft decisions is to list out all possibilities of s and compute associated metrics. This method has a very high complexity which scales as O(M2), where M is the constellation size and is considered to be impractical. A better approach was consequently developed in U.S. patent application Ser. No. 11/857,269, inventors: Prasad et al., entitled “Max_Log Receiver For Multiple Input Multiple output (MIMO) Systems”. In this technique, the demodulator involves twice linearly transforming the received signal vector to obtain new transformed vectors that can be modeled as in the above Equation, but where the transformed channel matrices have a triangular structure. The transformed vectors are then used for metric computations after exploiting the induced triangular structure in the transformed channel matrices. Determining the matrices used for these two linear transformations as well as the elements of the resulting transformed channel matrices involves square-root operations that are costly to implement.
Accordingly, there is a need for an efficient square-root free 2 symbol max-log receiver.